To find the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex], follow these steps:
1. Express the function [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
Start with the given function:
[tex]\[ y = 2x + 1 \][/tex]
2. Switch [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
To find the inverse function, we swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 2y + 1 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
- First, subtract 1 from both sides to isolate the term involving [tex]\( y \)[/tex]:
[tex]\[ x - 1 = 2y \][/tex]
- Next, divide both sides by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{x - 1}{2} \][/tex]
4. Simplify the expression:
- Distribute the division:
[tex]\[ y = \frac{1}{2}x - \frac{1}{2} \][/tex]
So, the inverse function is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
Therefore, the correct answer is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
